Quadratic Expression that is always positive

Quadratic Expression that is always positive

IP 3
  1. Find the range of values of \(k\) for which \(5{{x}^{2}}-3x+k\) is always positive.
  2. Find the range of values of \(k\) for which \(2{{x}^{2}}+{{k}^{2}}+2-2(k+2)x\) is always positive.

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Answer:(a) \(k>\frac9{20}\) (b) \(k<0\) or \(k>4\)

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